Yes, of course aperson with autism can get a gun. There are no restrictions on autistic people when it comes to purchasing guns.
Anywhere where it is legal to own a gun - there are no restrictions on autistic people owning or operating guns.
There's no such thing as a mild form of Autism - a person is either Autistic or they're not, how they're effected can be mildly but this can change throughout their lives. There are no restrictions on Autistic people owning a gun, as long as they have the capacity for responsible gun ownership.
An Autistic is a person with Autism.
If there's any record of it, no.
A person does not 'develop' autism - a person is born autistic.
A person does not 'develop' autism - a person is born autistic.
A person does not develop autism. Autism is a neurological difference, as such it starts within the womb during the second trimester when the brain is being formed.
Someone who is born on the autism spectrum/has autism spectrum disorder/is autistic. Often used in an offensive manner towards autistic people.
I'm going to guess, in the United States, no, not legally. One of the ineligible classes for owning a gun is defined as: any person/people "adjudicated as mental defectives or incompetents or those committed to any mental institution." I don't enough about Autism to define it, but I suspect it falls into that category. As long as you have a gun permit then you can have a gun. And you can have autism.
The eyes of a person with autism look the same as the eyes of other people.
A person does not develop autism, autism is not something that occurs to neurotypical people, in the same way that a white person doesn't develop into another race. A person is born autistic, their brains form in the womb.
A teenager doesn't develop autism - a person is autistic from birth.
Autism can be inherited from parents with genes for autism. Autism can also be the result of the spontaneous mutation of a gene. It is suspected that a person with the genes for autism might need an environmental factor (in the womb or shortly after birth) to trigger the development of autism.